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G C Rota

Publications and source records attributed to G C Rota.

13 recordsLinked to original sources
PubMed1994

Plethystic Hopf algebras.

The notion of a plethystic algebra associated with a Hopf algebra endowed with a suitable bilinear form is defined. A special case is the Hopf algebra of symmetric functions.

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PubMed1994

Plethystic algebras and vector symmetric functions.

An isomorphism is established between the plethystic Hopf algebra Pleth(Super[L]) and the algebra of vector symmetric functions. The Hall inner product of symmetric function theory is extended to the Hopf algebra Pleth(Super[L]).

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PubMed1993

On the span of supersymmetric Young tableaux.

De Concini et al. [De Concini, C., Eisenbud, D. & Procesi, C. (1980) Invent. Math. 56, 129-165] have established for classical Young bitableaux the fact that the span of all bitableaux of shape lambda over the rationals includes all bitableaux of all shapes mu > lambda. We extend their result to the more general setting of supersymmetric Young tableaux. Our proof, even in the classical case, has the advantage of providing an explicit combinatorial algorithm for the computation of the coefficients.

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PubMed1991

Theory of symmetry classes.

Although a great deal of work has gone into construction of the irreducible representations of the symmetric group n (and of the general linear group) a simple, intuitive characterization of the symmetry classes is missing. Relying on a systematic distinction between permutations of variables and permutations of places, we provide two such characterizations, showing that elements belonging to any such symmetry class can be described in one of two ways: (i) as the solutions of explicitly given (though not independent) sets of linear equations or (ii) as linear combinations of "simple" elements of a given symmetry class, a simple element being a generalization to an arbitrary symmetry class of the notion of a decomposable skew-symmetric tensor.

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PubMed1990

Supersymmetric Hilbert space.

A generalization is given of the notion of a symmetric bilinear form over a vector space, which includes variables of positive and negative signature ("supersymmetric variables"). It is shown that this structure is substantially isomorphic to the exterior algebra of a vector space. A supersymmetric extension of the second fundamental theorem of invariant theory is obtained as a corollary. The main technique is a supersymmetric extension of the standard basis theorem. As a byproduct, it is shown that supersymmetric Hilbert space and supersymplectic space are in natural duality.

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PubMed1989

Standard basis in supersymplectic algebras.

An integral standard basis is given for products of Pfaffians containing positively and negatively signed variables. Applications to invariant theory are derived.

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PubMed1986

Symbolic method in invariant theory.

A symbolic method based on an extension of the straightening algorithm is developed for the representation of joint invariants of symmetric and skew-symmetric tensors. For skew-symmetric tensors, the method holds over infinite fields of arbitrary characteristic.

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